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## Homework Statement

Given an electrical dipole of electrical dipole momentum [tex]\vec P = p\hat k[/tex], centered in [tex]0\hat i + 0\hat j + 0\hat k[/tex], find the potential in all the space, where [tex]V(\infty ) = 0[/tex]. If the dipole is now surrounded by a hollow spherical conductor (initially discharged), find the electrostatic field and potential outside the sphere.

## The Attempt at a Solution

I can find the [tex]\vec E[/tex] and V for all r for the dipole without the sphere: I find that [tex]V(\vec r) = \frac{{\vec P \cdot \vec r}}{{4\pi \varepsilon _0 r^3 }}[/tex]. But the problem comes with the spherical conductor. I can now use Gauss' Law, given that I can use a spherical surface for it. But the net charge inside that surface would be zero (given the dipole and the discharged spherical conductor). This got me thinking that there must be something wrong alltogether, because what I imagine happens is that in one side of the conductor outter surface there would be positive charge and on the other negative charge (due to the presence of the dipole). And that would generate an electrostatic field, similar to that of the dipole.

What am I doing wrong? Can I use Gauss' Law here?